Question

The sides of a right triangle containing the right angle are $\left(5x\right)cm$ and $(3x-1)cm$. If area of triangle be $60{cm}^2$, calculate the length of the sides of the triangle.

• A. $15cm,8cm,17cm$
• B. $16cm,8cm,17cm$
• C. $16cm,8cm,19cm$
• D. $18cm,8cm,14cm$

Answer 1

Answer: (A)

$15cm,8cm,17cm$

Given: In a right angled triangle, Perpendicular = 5x and Base = 3x - 1
Area = 60 $c{m}^2$
Area of triangle = $\frac{1}{2}\left(base\right)\left(height\right)$

$60=\frac{1}{2}\left(5x\right)(3x-1)$

$120=15x^2-5x$

$24=3x^2-x$

$3x^2-x-24=0$

$3x^2-9x+8x-24=0$

$3x(x-3)+8(x-3)=0$

$(3x+8)(x-3)=0$

$x=3,\frac{-8}{3}$

Neglect the nagative value, $x=3$
Thus, perpendicular = 15 cm and base = 8 cm

Now, from Pythagoras theorem,

$H^2=P^2+B^2$

$H^2={15}^2+8^2$

$H^2=225+64$

$H^2=289$

$H=17cm$